U.S. patent application number 12/986174 was filed with the patent office on 2011-05-05 for optimizing performance parameters for switchable polymer dispersed liquid crystal optical elements.
Invention is credited to Stephen A. Siwecki, Richard L. Sutherland, Vince P. Tondiglia.
Application Number | 20110102711 12/986174 |
Document ID | / |
Family ID | 34992668 |
Filed Date | 2011-05-05 |
United States Patent
Application |
20110102711 |
Kind Code |
A1 |
Sutherland; Richard L. ; et
al. |
May 5, 2011 |
Optimizing Performance Parameters For Switchable Polymer Dispersed
Liquid Crystal Optical Elements
Abstract
Described herein are the materials, mechanisms and procedures
for optimizing various performance parameters of HPDLC optical
devices in order to meet differing performance requirements. These
optimization tailoring techniques include control and independent
optimization of switchable HPDLC optical devices to meet the
demanding requirements of anticipated applications for, inter alia,
the telecommunications and display industries. These techniques
include optimization of diffraction efficiency, i.e., index
modulation, polarization dependence control, haze, cosmetic
quality, control of response and relaxation time, voltage driving
for on and off switching, and material uniformity. This control and
independent optimization tailors properties of switchable HPDLC
optical devices according to the specific requirements of the
application of the switchable HPDLC optical device. The invention
disclosed herein retains the desirable attributes of the
multi-functional acrylate system for forming HPDLC optical devices,
but adds new materials to the acrylate system and/or new process
control to the recording to optimize performance parameters as may
be needed for specific applications. This results in high optical
quality switchable holograms with good diffraction efficiency and
low, stable switching voltage.
Inventors: |
Sutherland; Richard L.;
(Dayton, OH) ; Siwecki; Stephen A.; (Dayton,
OH) ; Tondiglia; Vince P.; (Dayton, OH) |
Family ID: |
34992668 |
Appl. No.: |
12/986174 |
Filed: |
January 6, 2011 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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11399517 |
Apr 7, 2006 |
7872707 |
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12986174 |
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11129441 |
May 16, 2005 |
7072020 |
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11399517 |
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10408259 |
Apr 8, 2003 |
6950173 |
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11129441 |
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Current U.S.
Class: |
349/86 ;
349/141 |
Current CPC
Class: |
G02F 1/13342 20130101;
G02B 5/32 20130101; G03H 2250/38 20130101; G03H 1/22 20130101 |
Class at
Publication: |
349/86 ;
349/141 |
International
Class: |
G02F 1/1334 20060101
G02F001/1334; G02F 1/1343 20060101 G02F001/1343 |
Claims
1. A system for controlling the index modulation of a switchable
polymer dispersed liquid crystal optical element comprising: a
first substrate and a second substrate with a pre-polymer liquid
crystal material therebetween; and a first and a second electrode
pattern on each of the first and second substrates, wherein at
least one of the first and second electrode patterns consists of
interdigitated electrodes.
2. The system according to claim 1, wherein both of the first and
second electrode patterns consist of interdigitated electrodes; and
further wherein, the interdigitated electrodes of the first
electrode pattern are staggered with respect to the interdigitated
electrodes of the second electrode pattern.
3. The system according to claim 1, wherein at least one of the
first and second electrode patterns is a solid planar pattern.
4. The system according to claim 1, wherein each of the
interdigitated electrodes has a height (h) and each of the
interdigitated electrodes are separated by a separation (b),
wherein each of (h) and (b) are approximately equal to the width of
the polymer dispersed liquid crystal optical material.
5. The system according to claim 1, wherein the first electrode
pattern is transparent.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a divisional of U.S. patent application
Ser. No. 11/399,517, filed Apr. 7, 2006, which is a divisional of
U.S. patent application Ser. No. 11/129,441, filed May 16, 2005,
now U.S. Pat. No. 7,072,020, which is a divisional of U.S. patent
application Ser. No. 10/408,259, filed Apr. 8, 2003, now U.S. Pat.
No. 6,950,173. Each of the above-identified applications is
incorporated herein by reference in its entirety.
BACKGROUND OF THE INVENTION
[0002] 1. Field of the Invention
[0003] The purpose of this invention is to control and optimize the
performance parameters of switchable holograms to tailor the
properties to application-specific devices.
[0004] 2. Description of the Related Art
[0005] U.S. Pat. No. 5,942,157 provides a description of materials
and methods for producing switchable holographic Bragg
gratings.
[0006] U.S. Pat. Nos. 5,751,452 and 5,748,272 to Tanaka et al.
teach an optical device made from a switchable holographic polymer
dispersed liquid crystal (hereafter "PDLC") grating and methods for
fabricating the same. Tanaka et al teach the use of NOA65 (polyene
and polythiol mixture), but do not teach how it may be used in
conjunction with a multifunctional acrylate to reduce switching
voltage and eliminate voltage creep. In their teaching, NOA65 is
the sole polymerizable monomer in the described embodiments. These
embodiments are also found in U.S. Pat. Nos. 4,938,568 and
5,096,282 to Margerum et al.
[0007] U.S. Pat. No. 5,875,012, and European Patent Application
Nos. 98300541.1, 98300543.0, and 98300468.0 to Crawford et al.
teach reflective displays made with switchable PDLC holograms, but
provide little in the way of materials or methods for optimizing
performance. Crawford et al. teach the use of an anisotropic
polymer index-matched to the liquid crystal to reduce haze at large
viewing angles. This is also taught in U.S. Pat. Nos. 4,994,204 and
5,240,636 Doane et al.
[0008] U.S. Pat. No. 5,731,853 to Taketomi et al. and U.S. Pat. No.
6,083,575 Ninomiya et al. teach devices made with switchable PDLC
holograms, but provide no teaching for optimizing switchable
hologram performance.
[0009] U.S. Pat. No. 5,313,317 to Saburi et al. and U.S. Pat. Nos.
5,330,264 and 5,648,857 to Ando et al. teach beam control methods
for controlling unwanted gratings (i.e., "ghost holograms") in
non-PDLC holograms using particular geometrical arrangements.
[0010] Each of the above-identified references is incorporated by
reference herein in its entirety.
SUMMARY OF THE INVENTION
Summary of the Problem
[0011] Demand for information has become a strong driver in many
business, consumer, and government applications. Three key
components of this demand are the storage, transmission, and
display of information. The latter two in particular are placing
severe demands on available hardware and software. In
communications, there has been an explosion of traffic driven by
the Internet, business data, and digital image transfers. In the
end-point use of this huge data stream, visual utilization and
management of data have high priority. Large data content requires
high resolution (SVGA to XGA) along with full-color capability. The
technological response to these challenges has spawned several
innovations. For telecommunications applications, part of the
technological response is to provide higher data rates and
bandwidth extension through the use of dense wavelength division
multiplexing (DWDM). For easy visual access to information,
portable and handheld devices are evolving along with flat screens
and personal displays. In addition, efforts are underway to make
the advantages of DVD and HDTV available in these formats.
[0012] Optics is at the core of all of these technologies. The
information revolution is placing stringent demands on several
optical components. For example, short and long-period fiber Bragg
gratings are playing key roles in telecommunications, but the
demand for multiple wavelengths and the ability for dynamic
reconfiguration by DWDM is growing. In information display
applications, the use of portable and micro-displays, combined with
virtual display technology, is creating the need for complex
off-axis optical systems in very compact, lightweight packages.
This becomes impossibly heavy and cumbersome with conventional
refractive and reflective optics.
[0013] Diffractive optics is the natural response to many of these
demands. But these devices are by their very nature monochromatic.
Multi-wavelength and dynamic reconfiguration capabilities are
forcing a reconsideration of the use and fabrication of diffractive
optical elements to satisfy the growing needs of the information
revolution.
[0014] Switchable holographic optical elements (HOEs) have been
invented to fulfill the promise of diffractive optics in meeting
the technological challenges in telecommunications and information
display. Multi-layered switchable holographic optical elements in a
single solid-state device form a substitute for multiple static
elements and complex refractive/reflective optical systems. This
dramatic innovation has prompted one technology developer to coin
the phrase "an optical system in a chip" as an apt description of
switchable HOEs.
[0015] To be successful, switchable hologram technology must
present a flexible approach to optical element design and
fabrication, offering high efficiency and optical quality with low
power consumption. Moreover, it must be tailored to customer
specifications, i.e., it has to be very application-specific. For
example, devices in telecommunications applications that require
specific wavelength and format considerations include
reconfigurable add/drop switches, multiplexers, optical cross
connects, optical switches, wavelength selectors and tuners, and
spectral attenuators or gain flatteners. Examples of such needs
also abound in the information display area, including personal
DVD/HDTV viewers, portable displays, data phone/handheld Internet
displays, wearable PC displays, digital picture frames, desktop
telephone E-mail/Internet displays, ultra-portable projection
systems, and desktop monitors.
Summary of the Solution
[0016] Polymer-dispersed liquid crystal ("PDLC") holographic
materials have now been successfully demonstrated in several
components and prototype devices. These components and devices
offer a solution to the need for an electronically driven,
multi-layer, multi-wavelength, complex optical system in a thin,
lightweight, low-electrical-power element. The fabrication of
switchable holograms by the photopolymerization-induced phase
separation of liquid crystal ("LC") from an initially homogenous
pre-polymer mixture has been discussed in commonly owned U.S. Pat.
No. 5,942,157. Prior to forming the hologram thereon, the
pre-polymer mixture consists of a multi-functional acrylate monomer
(or mixture of multi-functional monomers of differing
functionality) combined with a mono-functional aromatic vinyl
monomer and a LC, along with other key ingredients, including a
photoinitiator dye. Similarly, the holographic recording process
has also been described, employing a single-step method wherein
coherent laser beams combine to form an interferogram in the plane
of the pre-polymer mixture. As the system cures, the LC phase
separates to form the hologram, consisting of a pure grating or
mixture of gratings. These gratings are comprised of alternating
LC-rich and polymer-rich regions.
[0017] As these switchable holographic materials and devices near
application in the markets discussed above, it is becoming clear
that several performance parameters are critical to the success of
the devices employing this technology. For example, various
applications of the switchable holographic-PDLC (hereafter "HPDLC")
optical elements require polarized light, while others require
diffraction of unpolarized light. Consequently, there is an
advantage to having the capability to control the polarization
dependence of the PDLC grating for specific applications.
[0018] Further, in many applications with holograms, haze is a
problem. In HPDLC optical elements, haze is produced by light
scattering from inhomogeneities in the HPDLC film component of the
optical element. Some of these inhomogeneities are contaminants
that can be controlled by careful processing. Others, however,
originate from the phase-separated LC droplets. The diffraction
planes themselves will produce some random scattering due to
nonuniform distributions of LC droplets from plane to plane.
However, a major source of scattering comes from phase-separated
droplets that occur outside the desired Bragg planes. Examples of
this are cross-gratings and diffraction rings formed by spurious
reflections and diffraction of the recording beams. Also, in some
cases LC may randomly phase separate in the polymer-rich regions.
Scattering is a strong function of droplet size and density. In
some cases, a haze as large as 10% has been measured. It is
strongly desired to reduce and control the amount of haze in
holograms for specific applications.
[0019] Further still, in electrically switchable holograms,
minimization and control of power dissipation is an important
consideration. Power dissipation leads to joule heating, which in
some cases can cause problems with thermal stability. Also, large
power consumption requires a more expensive electrical power supply
and possibly larger voltages, which may lead to electrical shorting
that destroys the hologram's usefulness. This depends largely on
the switching voltage of the hologram. High switching voltage leads
to large current drawn from the power supply. In switchable PDLC
gratings, power consumption and dissipation comes from current
drawn to charge up the transparent electrodes, as well as from
resistive heating in the transparent electrodes and through the
hologram, due to a finite conductivity of the PDLC material.
[0020] Switching speed requirements of the HPDLC optical elements
depends on the intended application. Some applications may require
on/off-switching times in the microsecond regime, while some may
only require millisecond response. Consequently, it is useful to
have the ability to tailor the switching speed to the application
in order to optimize other parameters, such as switching
voltage.
[0021] Some applications for the HPDLC optical elements place the
elements in harsh environments that degrade its properties. Typical
environmental parameters that prove deleterious to operation
include temperature, humidity, and UV exposure, the most severe of
these being temperature. LCs nominally have freezing points below
0.degree. C. and nematic-to-isotropic (N-I) transition points at
65-100.degree. C. The high temperature range is usually the most
problematic in devices. Any contaminants or diluents in the LC will
lower the LC's order parameter and thereby reduce its N-I
transition. This in turn can significantly reduce diffraction
efficiency. For example, the N-I transition may be reduced by as
much as 30-40.degree. C. by such contaminants/diluents. This
severely restricts the operating temperature of the hologram.
Consequently, the ability to control the environmental
vulnerability of the HPDLC optical elements is desirable.
[0022] The current invention sets forth materials, mechanisms and
procedures for optimizing various performance parameters in order
to meet differing performance requirements. These optimization
tailoring techniques include control and independent optimization
of switchable HPDLC optical devices to meet the demanding
requirements of anticipated applications for, inter alia, the
telecommunications and display industries. These techniques include
optimization of diffraction efficiency, i.e., index modulation,
polarization dependence control, haze, cosmetic quality, control of
response and relaxation time, voltage driving for on and off
switching, and material uniformity. This control and independent
optimization tailors properties of switchable HPDLC optical devices
according to the specific requirements of the application of the
switchable HPDLC optical device. The invention disclosed herein
retains the desirable attributes of the multi-functional acrylate
system for forming HPDLC optical devices, but adds new materials to
the acrylate system and/or new process control to the recording to
optimize performance parameters as may be needed for specific
applications. This results in high optical quality switchable
holograms with good diffraction efficiency and low, stable
switching voltage.
[0023] A first embodiment of the present invention describes a
system for controlling the index modulation of a polymer dispersed
liquid crystal optical element. The system comprises a first
substrate and a second substrate with a pre-polymer liquid crystal
material therebetween; and a first and a second electrode pattern
on each of the first and second substrates, wherein at least one of
the first and second electrode patterns consists of interdigitated
electrodes.
[0024] A second embodiment of the present invention describes a
method for controlling the index modulation of a switchable polymer
dispersed liquid crystal optical component. The method comprises
providing a pre-polymer liquid crystal material between a first and
second substrate, the first and second substrate having a first and
second electrode pattern thereon, respectively, for applying a
switching voltage to the switchable polymer dispersed liquid
crystal optical component, wherein at least one of the first and
second electrode patterns consists of interdigitated electrodes;
applying a voltage approximately equal to the switching voltage to
every other interdigitated electrode, creating an in-plane electric
field within the pre-polymer liquid crystal material;
holographically irradiating the pre-polymer liquid crystal material
resulting in polymerization of the pre-polymer liquid crystal,
wherein liquid crystal droplets formed from the holographic
irradiation are formed with symmetry axes oriented in the same
direction as the in-plane electric field; and removing the voltage
approximately equal to the switching voltage once polymerization is
complete.
[0025] A third embodiment of the present invention describes an
inverse mode switchable grating system. The system comprises a
holographically polymerized polymer dispersed liquid crystal
material having a switchable grating formed therein; and at least a
first and a second electrode for applying a switching field to the
switchable grating in order to vary a diffraction efficiency
thereof, wherein application of the switching field increases the
diffraction efficiency of the switchable grating and removal of the
switching field decreases the diffraction efficiency of the
switchable grating.
[0026] A fourth embodiment of the present invention describes a
method for switching a holographic diffraction grating via a
switching field between a first diffraction efficiency and a second
diffraction efficiency. The method comprises orienting the
holographic diffraction grating such that an internal angle of
p-polarized light incident thereon satisfies the following
condition for a switching field of zero,
tan .theta. .rho. = ( xx ( 1 ) zz ( 1 ) ) 1 / 2 ##EQU00001##
wherein .theta..sub..rho. is the angle of incidence of a reference
wave of the incident light and .di-elect cons..sub.xx.sup.(1) and
.di-elect cons..sub.zz.sup.(1) are the x and z components of the
modulation of the dielectric tensor for a material comprising the
holographic diffraction grating and the holographic diffraction
grating has a first diffraction efficiency; and applying a
switching field greater than zero in order to switch the
holographic diffraction grating to a second diffraction
efficiency.
[0027] A fifth embodiment of the present invention describes a
method for splitting a light beam. The method comprises receiving a
light beam at a holographically polymerized polymer dispersed
liquid crystal material having an electrically controllable
switchable grating formed therein; and controlling the application
of an electric field to the switchable grating, wherein when no
electric field is applied to the switchable grating the light beam
is split into s-polarized light that is reflected from the
switchable grating and p-polarized light that is transmitted
through the switchable grating and further wherein when a threshold
switching electric field is applied to the switchable grating the
light beam is split into s-polarized light that is transmitted
through the switchable grating and p-polarized light that is
reflected from the switchable grating.
[0028] A sixth embodiment of the present invention describes a
method for controlling the haze in a holographically polymerized
polymer dispersed liquid crystal optical element. The method
comprises forming a loosely gelled network within a pre-polymerized
polymer dispersed liquid crystal material and holographically
polymerizing the polymer dispersed liquid crystal material,
including the loosely gelled network, to form the polymer dispersed
liquid crystal optical element with decreased haze.
[0029] A seventh embodiment of the present invention describes a
method for forming a holographically polymerized polymer dispersed
liquid crystal optical element with reduced haze. The method
comprises adding a pre-polymerized polymer dispersed liquid crystal
material to a pre-existing loosely gelled network; placing the
pre-existing loosely gelled network containing the pre-polymerized
polymer dispersed liquid crystal material between first and second
transparent substrates; and interfering a first beam and a second
beam within the pre-existing loosely gelled network containing the
pre-polymerized polymer dispersed liquid crystal material to form
the holographically polymerized polymer dispersed liquid crystal
optical element with reduced haze.
[0030] An eighth embodiment of the present invention describes a
method for driving a polymer dispersed liquid crystal hologram. The
method comprises providing a polymer dispersed liquid crystal
hologram between a first and second substrate, the first and second
substrate having a first and second electrode pattern thereon,
respectively, for applying a switching voltage to the polymer
dispersed liquid crystal hologram, wherein the first and second
electrode patterns consist of interdigitated electrodes; applying a
first voltage scheme, wherein a voltage approximately equal to the
switching voltage is applied to the interdigitated electrodes on
the first substrate and the interdigitated electrodes on the second
substrate are connected to ground in order to drive the polymer
dispersed liquid crystal hologram off; and removing the first
voltage scheme and applying a second voltage scheme, wherein a
voltage approximately equal to the switching voltage is applied to
every other interdigitated electrode on the first and second
substrates and the intermittent electrodes therebetween are
connected to ground in order to drive the polymer dispersed liquid
crystal hologram on.
BRIEF DESCRIPTION OF THE FIGURES
[0031] In the Figures:
[0032] FIG. 1 shows a conventional diffraction geometry for a Bragg
transmission grating;
[0033] FIG. 2 shows a model depicting the diffraction and
polarization properties of light in a HPDLC optical device
according to an embodiment of the present invention;
[0034] FIG. 3 shows the distribution of symmetry axes in LC domains
of a HPDLC optical element according to an embodiment of the
present invention;
[0035] FIG. 4 shows the orientation of a LC domain symmetry axis in
the presence of an electric field according to an embodiment of the
present invention;
[0036] FIG. 5 shows the orientation of an LC droplet director N
relative to a laboratory reference frame xyz according to an
embodiment of the present invention;
[0037] FIGS. 6a and 6b show the form of distribution functions used
in an analysis of certain embodiments of the present invention;
[0038] FIGS. 7(a) through 7(c) show the LC droplet direction
distributions according to an embodiment of the present
invention;
[0039] FIGS. 8(a) and 8(b) show coupled wave interaction for
reflection and transmission gratings, respectively, according to
embodiment of the present invention;
[0040] FIG. 9 shows electric field effects on diffraction
efficiency of a grating at normal incidence according to an
embodiment of the present invention;
[0041] FIG. 10 shows a switching curve of a grating at normal
incidence according to an embodiment of the present invention;
[0042] FIG. 11 shows the difference in switching behavior between
normal and off-incidence radiation on a grating according to an
embodiment of the present invention;
[0043] FIG. 12 shows the switching of p-polarized and s-polarized
light according to an embodiment of the present invention;
[0044] FIGS. 13a and 13b show electrode configurations for aligning
LC droplets during formation of a HPDLC optical element according
to an embodiment of the present invention;
[0045] FIG. 14 shows a voltage scheme for aligning the LC droplets
of a HPDLC optical element according to an embodiment of the
present invention;
[0046] FIG. 15 shows a conventional transmission hologram prepared
without pre-exposure;
[0047] FIG. 16 shows a diffraction efficiency comparison according
to an embodiment of the present invention;
[0048] FIG. 17 shows a hologram recording set-up according to an
embodiment of the present invention;
[0049] FIGS. 18a and 18b show voltage schemes for switching a HPDLC
optical element according to an embodiment of the present
invention; and
[0050] FIG. 19 shows a voltage drive waveform for switching a HPDLC
optical element according to an embodiment of the present
invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS OF THE PRESENT
INVENTION
[0051] The preferred embodiments of the present invention utilize
the materials and/or process controls as set forth in the second
column of Table 1 in order to optimize the corresponding
performance parameters of the first column of Table 1.
TABLE-US-00001 TABLE 1 Performance Parameters Materials/Process
Control Diffraction efficiency Nematic director control (index
modulation) Fringe stability/contrast Gel network pre-stabilization
Polarization dependence Nematic director control Haze Gel network
pre-stabilization Index matching (Fresnel reflections &
scattering) Cosmetic quality Gel network pre-stabilization Index
matching (Fresnel reflections & scattering) Inverse mode
switching Anisotropic grating parameters Switching contrast ratio
LC droplet size/shape (dynamic range) Response/relaxation time LC
droplet size/shape Electrode design/voltage drive scheme
[0052] In order to provide a context for the implementation of the
optimization materials and techniques of the preferred embodiments
of the present invention, the base features of the HPDLC optical
devices are described below. The HPDLC optical devices consist of a
homogeneous mixture of ingredients (i.e., "pre-polymer material")
that includes the following: a polymerizable monomer (mixture of
multi-functional acrylates, including at least a pentaacrylate),
liquid crystal ("LC") material (typically a mixture of
cyanobiphenyls), a photoinitiator dye (one dye with absorption
spectrum overlapping recording laser wavelength), a co-initiator, a
reactive diluent (formerly called cross-linking agent), and a
surfactant-like additive (formerly called surfactant). Specific
examples of the homogeneous mixtures, as well as other formation
process and material descriptions supporting the embodiments
described herein are found in U.S. Pat. No. 5,942,157 and U.S.
patent application Ser. No. 09/033,512 entitled "Switchable Volume
Hologram Materials and Devices," filed Mar. 2, 1998; Ser. No.
09/033,513 entitled "Switchable Volume Hologram Materials and
Devices," filed Mar. 2, 1998; Ser. No. 09/033,514 entitled
"Switchable Volume Hologram Materials and Devices," filed Mar. 2,
1998; Ser. No. 09/034,014 entitled "Switchable Volume Hologram
Materials and Devices," filed Mar. 2, 1998; Ser. No. 09/429,645
entitled "Switchable Volume Hologram Materials and Devices," filed
Oct. 29, 1999; Ser. No. 09/347,624 entitled "Switchable Volume
Hologram Materials and Devices," filed Jul. 2, 1999; Ser. No.
09/363,169 entitled "Electrically Switchable Optical Couplers and
Reconfigurable Optical Polymer Dispersed Liquid Crystal Materials
Including Switchable Optical Couplers and Reconfigurable Optical,"
filed Jul. 29, 1999; Ser. No. 09/742,397 entitled "Switchable
Polymer-Dispersed Liquid Crystal Optical Elements," filed Dec. 22,
2000; Ser. No. 09/577,166 entitled "Volume Hologram Replication
System and Method for Replicating Volume Holograms," filed May 24,
2000; and Ser. No. 10/303,927 entitled "Tailoring Material
Composition for Optimization of Application-Specific Switchable
Holograms" filed Nov. 26, 2002; and U.S. patent application Ser.
Nos. 09/033,512, 09/033,513, 09/033,514, 09/034,014, 09/429,645,
09/347,624, and 09/363,169, each of which is incorporated by
reference herein in its entirety.
[0053] When the pre-polymer material is irradiated holographically,
the photoinitiator absorbs light in the bright fringes and reacts
with the co-initiator, creating free radicals. The free radicals
then initiate polymerization of the multi-functional acrylates. The
free-radical process is very fast, and a three-dimensional polymer
network is created in just a few seconds. This rapid development of
a densely cross-linked network is critical to the phase separation
of small LC droplets in the dark fringes, which is what establishes
the hologram. Highly functional acrylates are needed in order to
produce this with a minimal exposure time. A short exposure time is
important in holography to reduce the effects of unwanted
vibrations and other perturbations that tend to wash out the index
modulation, and to make the process more amenable to mass
production. In addition, the resulting rapid polymerization and
phase separation are favorable for the formation of small LC
droplets, which reduces random scattering losses (i.e., haze). The
surfactant further contributes to reducing LC droplet size,
yielding an optically clear hologram.
[0054] The three-dimensional network that results from the
acrylates contributes to "squeezing" the LC out into a separate
phase and to yielding desirable optical properties for the
hologram. In fact, the hologram and its switchability would not be
possible without these elastic attributes of the polymer. However,
these strong elastic forces also make the polymer matrix very
stiff. The stiffness contributes to a high switching voltage for
the HPDLC optical devices. Moreover, the multi-functionality leads
to continual post-polymerization after the hologram recording is
completed. This stiffens the matrix further and slowly drives the
switching voltage up. This is referred to as voltage creep. In some
cases the voltage creep can increase the switching voltage by as
much as 100%. The elastic relaxation of the multi-functional
acrylate system also produces another phenomenon: shrinkage. This
can be seen in reflection holograms where the wavelength of the
Bragg reflection peak will blue shift due to shrinkage of the
grating period. Although not completely understood, it appears that
shrinkage has a major effect in a direction parallel to the grating
vector. Hence, in reflection gratings, this reduces the grating
period, which can in most cases be compensated by appropriate
recording conditions (e.g., compensating recording angles).
However, there appears to be a more deleterious effect in
transmission holograms where the grating vector is in the plane of
the hologram. Shrinkage in the plane of the hologram while
recording appears to produce non-uniformity in the hologram. The
shrinkage is not uniform, but creates elastic instability in the
system, causing it to deform. This can almost be described as a
"wrinkling" of the hologram with concomitant non-uniformity in the
diffraction efficiency and cosmetic defects in the hologram's
appearance.
[0055] HPDLC optical devices also exhibit unique polarization
dependence. In FIG. 1, we show incident and diffracted beams with
two different polarization states: (a) perpendicular to the plane
containing the incident, diffracted, and grating wavevectors
(commonly known as s-polarization), and (b) in this plane (commonly
known as p-polarization). In prior art switchable Bragg
transmission grating 10, an incident beam of light 12 is deflected
by a diffraction grating 14 over a considerable angle that is equal
to twice the Bragg angle for the wavelength of incident light,
producing a diffracted exit beam 16. It is well known that for an
ordinary grating, s-polarized light will have a stronger coupling
(and hence larger diffraction efficiency) than p-polarized light.
The reason is that there is a complete overlap of the electric
field vectors for the incident and diffracted waves for
s-polarization independent of angle of incidence. The overlap of
p-polarized beams depends on the angle between the two beams, going
from complete overlap for 0.degree. angle to zero overlap for a
90.degree. angle. Hence, for an ordinary grating, the diffraction
efficiency of p-polarized light should never exceed that of
s-polarized light.
[0056] However, in PDLC gratings of the type in FIG. 1 the opposite
occurs: the diffraction efficiency of p-polarized light always
exceeds that of s-polarized light. Therefore, in the type of PDLC
grating considered in FIG. 1, there is a built-in anisotropy that
favors diffraction of light polarized in the plane containing the
wavevectors and the grating vector, even though the overlap of
field vectors is smaller for this case than for the perpendicular
polarization.
[0057] A simple model can explain these results, the LC phase
separates as uniaxial domains 20 with symmetry axis pointed
preferentially along the grating vector 22 as shown in FIG. 2. The
resulting domain 20 has an extraordinary index of refraction
n.sub.e along this symmetry axis, and a smaller ordinary refractive
index n.sub.o perpendicular to the axis. Since p-polarized light
has a component of its electric field along the symmetry axis, it
sees a refractive index heavily weighted by n.sub.e, and thus sees
a relatively large index modulation. On the other hand, s-polarized
light sees a refractive index weighted more by n.sub.o, and hence
experiences a relatively small index modulation
(n.sub.e>n.sub.o). Experimentally, the diffraction efficiency of
s-polarized light is considerably weaker than that of p-polarized
light. The symmetry axes of LC domains 20 are not perfectly aligned
with the grating vector 22. There is some small statistical
distribution 25 of the axes about this direction. The average of
the statistical distribution 25 points along the grating vector 22
as shown in FIG. 3. The average points along the grating vector.
Thus, s-polarized light will see a small amount of n.sub.e mixed in
with n.sub.o, which is what gives it its weak but measurable
diffraction efficiency. We note that when a strong electric field
24 is applied perpendicular to the plane of the grating vector 22,
as shown in FIG. 4, nearly all LCs reorient in a direction along
the beam propagation for some field value, and both s and
p-polarized light see the same index in the LC domains 20,
approximately equal to n.sub.o. Since this index nearly matches the
index of the surrounding polymer, the index modulation for both
polarization states disappears. The grating is said to be switched
"off." Additionally, as the field strength is further increased,
the LCs will eventually orient parallel to the field and thus not
be in an orientation to yield zero index modulation. Hence, the
diffraction efficiency goes through a minimum near zero and then
increases slightly with increasing field.
[0058] LC droplets form as nanoscale domains in HPDLC gratings.
Detailed studies by scanning electron microscopy (SEM) have
revealed that these domains can be roughly ellipsoidal, but are
quite often irregularly shaped. The nematic configuration of LC
molecules in micrometer scale droplets has been successfully
predicted in computer simulations and observed by optical
microscopy. A common arrangement of nematic directors in a
spherical droplet is the so-called bipolar configuration, which has
an axis of symmetry along a diameter and two point defects at the
polls. Computer simulations reveal that a similar pattern is
obtained in slightly elongated droplets. The nematic configuration
in nanoscale domains is more elusive. However, nuclear magnetic
resonance spectroscopy of deuterated-LC samples suggests that LC
domains may contain a line defect along their long axes. Optically,
these droplets appear to possess an axis of symmetry and behave as
uniaxial domains.
[0059] A model was developed for the behavior of elongated LC
droplets subjected to an electric field as described in Wu et al.
Liq. Cryst. 5, 1453 (1989) which is incorporated herein by
reference in its entirety. This model ignored the details of the
nematic configuration and assumed that the droplet is characterized
by a single vector, which they called the droplet director N. In
the absence of an electric field, N coincides with the symmetry
axis, which is also the major axis of the elongated droplet. This
uniaxial domain has a dielectric anisotropy that is approximately
equal to that of the bulk LC. Therefore, in the presence of an
electric field N will attempt to reorient along the direction of
the applied field. This reorientation is resisted by an elastic
torque, which arises due to the elastic distortion produced by the
applied field. The elastic torque is related to the local radius of
curvature and some average elastic force constant of the droplet. A
new equilibrium orientation of N is established by the condition
that the elastic restoring torque balances the electrical torque.
It is assumed that nanoscale LC droplets can be treated in the same
way and this model is also applied to HPDLC gratings.
[0060] Assuming the LC droplets are uniaxial domains, they can be
characterized by a diagonal dielectric tensor in the reference
frame of the droplet. Let .di-elect cons..sub..perp. and .di-elect
cons..sub..parallel. be the dielectric constants perpendicular and
parallel to N, respectively. At optical frequencies, the respective
refractive indices are given by n.sub..perp.=(.di-elect
cons..sub..perp./.di-elect cons..sub.0).sup.1/2 and
n.sub..parallel.=(.di-elect cons..sub..parallel./.di-elect
cons..sub.0).sup.1/2, where .di-elect cons..sub.0 is the
permittivity of free space. Because the nematic director
configuration is not uniform within the droplet, it is expected
that n.sub..perp.>n.sub.o and n.sub..parallel.<n.sub.e, where
n.sub.o and n.sub.e are the ordinary and extraordinary refractive
indices, respectively, of the bulk LC.
[0061] The orientation of the droplet director N relative to a
laboratory reference frame xyz is illustrated in FIG. 5. The
electric field is assumed to be applied along the z axis as shown.
The orientation of N is described by spherical angles .theta. and
.phi. in the laboratory frame. The model of Wu et al. predicts that
the field dependent equilibrium angle of N is given by
.theta. ( u , E ) = 1 2 tan - 1 [ 2 u 1 - u 2 2 u 2 - 1 + ( E / E c
) 2 ] ( 1 ) ##EQU00002##
where u=cos .theta..sub.0, with .theta..sub.0 the polar angle in
the absence of an applied field, E is the electric field strength,
and E.sub.c is a critical field for switching. Notice that the
azimuth angle .phi. is unchanged by the field.
[0062] In the laboratory reference frame the droplet dielectric
tensor .di-elect cons..sub.d is given by
d = R - 1 ( .perp. 0 0 0 .perp. 0 0 0 || ) R ( 2 ) ##EQU00003##
where R is the rotation matrix that transforms the laboratory
coordinate frame into the droplet coordinate frame, given by
R = ( cos .theta.cos .phi. cos .theta. sin .phi. - sin .theta. -
sin .phi. cos .phi. 0 sin .theta.cos .phi. sin .theta.sin .phi. cos
.theta. ) ( 3 ) ##EQU00004##
and R.sup.-1=R.sup.T is the inverse (transpose) of R. Explicitly,
the droplet dielectric tensor is
d = ( .perp. + .DELTA. sin 2 .theta. cos 2 .phi. .DELTA. sin 2
.theta. sin .phi.cos .phi. .DELTA. sin .theta. cos .theta.cos .phi.
.DELTA. sin 2 .theta. sin .phi.cos .phi. .perp. + .DELTA. sin 2
.theta. sin 2 .phi. .DELTA. sin .theta. cos .theta. sin .phi.
.DELTA. sin .theta. cos .theta.cos .phi. .DELTA. sin .theta. cos
.theta. sin .phi. .perp. + .DELTA. cos 2 .theta. ) ( 4 )
##EQU00005##
where .DELTA..di-elect cons.=.di-elect
cons..sub..parallel.-.di-elect cons..sub..perp., .theta. is given
by Eq. (1), and .phi.=.phi..sub.0 and .theta..sub.0 are constants
for a given droplet. The droplet directors N for an ensemble of
droplets are distributed about some mean orientation direction
given by and .phi..sub.0 relative to the laboratory reference
frame. The effective tensor modulation seen by light will be
related to an average over this ensemble. The azimuth angle range
is restricted from 0 to .pi. since the range from 0 to 2.pi.
includes -N, which is equivalent to N. In this analysis it is
assumed that N has a symmetric distribution about .theta.=.pi./2
and .phi.=.pi./2. In an alternative embodiment, the orientational
distribution may be skewed if some external force (e.g., shear) is
applied to orient the droplets preferentially in some particular
direction. In the present embodiment, it is assumed that the
distribution function forms naturally, with no external influence,
and has a symmetry that is dictated by the direction of the grating
vector and the naturally occurring orientation of droplet directors
relative to this vector. Additionally, in cases of slanted or
curved gratings it may not be possible to assume symmetric
orientational distributions, consequently, for these gratings
additional assumptions must be made. The model described herein is
useful to describe unslanted, planar reflection and transmission
gratings. The immediate consequence of a symmetric distribution
function is that all off-diagonal elements of the average droplet
dielectric tensor vanish. This is because the off-diagonal elements
in Eq. (4) are odd in either .theta. or .phi. about .pi./2.
[0063] For any given field strength E, each droplet will
independently assume a new equilibrium orientation, described by
Eq. (1), that is parameterized by its initial polar angle
.theta..sub.0. The azimuth angle will remain a constant determined
by its initial value .phi..sub.0. Hence the average tensor elements
can be found by averaging over the initial orientation angles
.theta..sub.0 and .phi..sub.0 by factoring the distribution
function into two functions, one dependent on .theta..sub.0 (or u)
only and one dependent on .phi..sub.0 only. Calling these
normalized distribution functions p(u) and q(.phi..sub.0),
respectively, the average diagonal tensor elements for the droplet
can be written as
.di-elect cons..sub.dx=.di-elect cons..sub..perp.+.DELTA..di-elect
cons..intg..sub.0.sup..pi..intg..sub.-1.sup.1
sin.sup.2.theta.(u,E)cos.sup.2.phi..sub.0p(u)q(.phi..sub.0)dud.phi..sub.0
(5)
.di-elect cons..sub.dy=.di-elect cons..sub..perp.+.DELTA..di-elect
cons..intg..sub.0.sup..pi..intg..sub.-1.sup.1
sin.sup.2.theta.(u,E)sin.sup.2.phi..sub.0p(u)q(.phi..sub.0)dud.phi..sub.0
(6)
.di-elect cons..sub.dz=.di-elect cons..sub..perp.+.DELTA..di-elect
cons..intg..sub.-1.sup.1 cos.sup.2.theta.(u,E)p(u)du (7)
It can be seen that these tensor elements depend on E through
.theta.(u,E).
[0064] The form of the distribution functions is not known a priori
and must be guessed. However, it is generally true that when
dealing with a large number of statistically independent objects,
the statistics of the ensemble tend to approximately obey a
Gaussian distribution. Accordingly, make the assumption that
p ( u ) = A exp ( - ( u - u _ ) 2 2 .sigma. u 2 ) ( 8 ) q ( .phi. 0
) = B exp ( - ( .phi. 0 - .phi. _ 0 ) 2 2 .sigma. .phi. 2 ) ( 9 )
##EQU00006##
where ( .phi..sub.0) is the mean value of u (.phi..sub.0),
.sigma..sub.u (.sigma..sub..phi.) is the standard deviation of the
u (.phi..sub.0) distribution, and A and B are appropriate
normalization constants. Since the variables in this case are
periodic and hence do not extend to .+-..infin., care must be taken
in defining the normalization constants. If the standard deviation
is small, the limits of integration in Eqs. (5)-(7) may be extended
to .+-..infin. though, and the distributions will look like
ordinary Gaussian functions. However, to retain the possibility
that the standard deviations are not that small and that the
distributions may tend toward constant values representing
isotropic orientation functions, compute the normalization
constants by integrating Eqs. (8) and (9) over the appropriate
range of variables and set the values equal to 1. FIGS. 6a and 6b
illustrate the form of the distribution functions used in this
analysis. For example, if the distributions are centered about mean
values =0 and .phi..sub.0=.pi./2, then the normalization constants
in Eqs. (8) and (9) become
A = 2 2 .pi. .sigma. u [ erf ( 1 + u _ 2 .sigma. u ) + erf ( 1 - u
_ 2 .sigma. u ) ] B = 2 2 .pi. .sigma. .phi. [ erf ( .phi. _ 0 2
.sigma. .phi. ) + erf ( .pi. - .phi. _ 0 2 .sigma. .phi. ) ] where
( 10 ) erf ( s ) = 2 .pi. .intg. 0 s exp ( - t 2 ) t ( 11 )
##EQU00007##
is the error function. Taking this approach, the values of the
means and standard deviations can be varied independently to study
the effects on diffraction efficiency and switching. They also give
an intuitive interpretation of the droplet director distribution
that is easy to visualize. For example, three distributions are
shown in FIGS. 7(a), 7(b) and 7(c), for an isotropic distribution
shown in FIG. 7(a), orientations clustered about the x axis, i.e.,
small .sigma..sub.u and .sigma..sub..phi., as shown in FIG. 7(b),
and about the xy plane, i.e., small .sigma..sub.u but isotropic in
.phi..sub.0, as shown in FIG. 7(c).
[0065] For a mixture of two homogeneous, isotropic materials the
effective dielectric constant of the medium can be expressed
approximately by .di-elect cons.=.di-elect cons..sub.a+f(.di-elect
cons..sub.b-.di-elect cons..sub.a), where .di-elect cons..sub.a and
.di-elect cons..sub.b are the dielectric constants of the host and
dispersed materials, respectively, and f is the volume fraction of
the dispersed material. This approximation holds as long as
.di-elect cons..sub.a.apprxeq..di-elect cons..sub.b. It is assumed
that this relation can be applied to an anisotropic HPDLC medium as
long as the dielectric tensors of the two materials are nearly
equal component by component. For the HPDLC grating, the volume
fraction f has the form of a periodic rectangular wave that is zero
in the solid polymer region, and has a value f.sub.c in the PDLC
region. The width of the PDLC region is .alpha..LAMBDA., where
.alpha. is a fraction (0.ltoreq..alpha..ltoreq.1) and .LAMBDA. is
the grating period. To apply coupled wave theory this distribution
is Fourier analyzed, keeping terms up to first order. The spatially
periodic dielectric tensor can thus be written as
( r ) = ( 0 ) + ( 1 ) cos ( K r ) ( 12 ) ( 0 ) = ( 1 - .alpha. f c
) p + .alpha. f c d ( 13 ) ( 1 ) = 2 f c .pi. sin ( .alpha..pi. ) (
d - p ) ( 14 ) ##EQU00008##
In these equations, K is the grating vector (|K|=2.pi./.LAMBDA.),
<.di-elect cons..sub.d> is the average LC droplet dielectric
tensor, and .di-elect cons..sub.p is the polymer dielectric tensor.
Assume that the polymer is isotropic so (.di-elect
cons..sub.p).sub.ij=.di-elect cons..sub.p.delta..sub.ij, where
.di-elect cons..sub.p is a scalar. Since <.di-elect
cons..sub.d> is diagonal, .di-elect cons..sup.(0) and .di-elect
cons..sup.(1) are also diagonal. Hence the laboratory frame also
serves as the principal axes frame of the medium. Equation (13)
yields the principal refractive indices of the medium,
n.sub.i=(.di-elect cons..sup.(0).sub.ii/.di-elect
cons..sub.0).sup.1/2 (i=x,y,z). In general, the medium is biaxial
(n.sub.x.noteq.n.sub.y.noteq.n.sub.z) and electro-optical through
the dependence of <.di-elect cons..sub.d> on E. The
components of Eq. (14) are the dielectric tensor modulation
elements that couple polarized optical waves in the diffraction
grating.
[0066] The coupled wave theory of Kogelnik et al., Bell Syst. Tech.
J. 48, 2909 (1969) was recently extended to anisotropic media G.
Montemezzani et al., Phys Rev. E. 55, 1035, (1997). Both of the
references are incorporated herein by reference. The interaction of
coupled waves in thick reflection and transmission holograms is
illustrated in FIGS. 8(a) and 8(b). For a reflection grating, the
grating vector is along the z axis as shown in FIG. 8(a), while for
a transmission grating it is along the x axis as shown in FIG.
8(b). A field is applied along the z direction in both cases. In
the Bragg regime, only the signal wave (.sigma.) and the reference
wave (.rho.) couple substantially. For an s-polarized wave, i.e.,
polarization perpendicular to the plane of incidence, the optical
field vector is along the y axis. For p-polarized light, i.e.,
polarization in the plane of incidence, the field vector lies in
the xz plane. The angle of incidence of the reference wave is
.theta..sub..rho. while the angle of diffraction of the signal wave
is .theta..sub..sigma.. These angles refer to the directions of the
Poynting vectors of the reference and signal waves, respectively. A
diagonal modulation tensor cannot couple s-polarized and
p-polarized waves. Hence the signal and reference waves will have
the same type of polarization (i.e., s or p). The coupling
coefficient may be written as
.kappa. = .pi. e ^ .sigma. ( 1 ) e ^ .rho. 2 0 ng .lamda. cos
.theta. .sigma. cos .theta. .rho. ( 15 ) ##EQU00009##
where .sub..sigma. ( .sub..rho.) is the unit vector of polarization
for the signal (reference) wave, and
n= {square root over (n.sub..sigma.n.sub..rho.)} (16)
with n.sub..sigma.(n.sub..rho.) the refractive index for the signal
(reference) wave. The parameter g is related to the walk-off angle
.delta. between the Poynting vector and wave vector and is given
by
g= {square root over (cos .delta..sub..sigma. cos
.delta..sub..rho.)} (17)
For unslanted gratings, n.sub..sigma.=n.sub..rho. and cos
.delta..sub..sigma.=cos .delta..sub..rho.. Notice that for an
unslanted reflection grating
.theta..sub..sigma.=.pi.-.theta..sub..rho., so cos
.theta..sub..sigma..ltoreq.0. For an unslanted transmission grating
.theta..sub..sigma.=2.pi.-.theta..sub..rho. and cos
.theta..sub..sigma..gtoreq.0. In unslanted gratings |cos
.theta..sub..sigma.|=cos .theta..sub..rho.. The explicit expression
of the coupling coefficient for s polarization is
.kappa. s = .pi. yy ( 1 ) 2 0 n y g s .lamda. cos .theta. .rho. (
18 ) ##EQU00010##
with g.sub.s=1, while for p polarization
.kappa. p = .pi. ( xx ( 1 ) sin 2 .theta. .rho. - zz ( 1 ) cos 2
.theta. .rho. ) 2 0 n ( .theta. .rho. ) g p .lamda. cos .theta.
.rho. ( 19 ) [ n ( .theta. .rho. ) ] - 2 = n x - 2 cos 2 .theta.
.rho. + n z 2 sin 2 .theta. .rho. and ( 20 ) g p = n x 2 cos 2
.theta. .rho. + n z 2 sin 2 .theta. .rho. [ ( n x 2 cos 2 0 .rho. +
n z 2 sin 2 0 .rho. ) 2 + ( n x 2 - n z 2 ) 2 sin 2 0 .rho. cos 2 0
.rho. ] 1 / 2 ( 21 ) ##EQU00011##
For weakly birefringent media (n.sub.x.apprxeq.n.sub.z),
g.sub.p.apprxeq.1.
[0067] In the case of reflection gratings, the peak diffraction
efficiency .eta..sub.j (j=s or p) of a reflection grating is
.eta..sub.j=tan h.sup.2(.kappa..sub.jL) (22)
At off-normal incidence (.theta..sub..rho..noteq.0) the coupling
coefficient is given by Eq. (18) for s polarization and Eqs.
(19)-(21) for p polarization.
[0068] Most of the LCs used in this analysis have similar values of
n.sub.o and n.sub.e. Hence the variation in diffraction efficiency
between different systems is primarily due to the parameters a and
f.sub.c, which are related to LC solubility for various types of
gratings and polymer systems, and to the distribution functions
p(u) and q(.phi..sub.0), which also appear to be dependent on the
type of grating and LC. In order to limit the variation of
parameters, the index n.sub.p can be measured for the polymer and
generally it is in the range of 1.52-1.54, depending on the amount
of LC remaining in solution in the polymer. For s-polarized light,
switching the grating to minimum diffraction efficiency implies
that n.sub..perp..apprxeq.n.sub.p (see the discussion below). Hence
the parameter n.sub..perp. can be fixed by this condition. The
quantities .alpha. and f.sub.c can be estimated from SEM studies of
HPDLC gratings. This leaves n.sub..parallel. and droplet
statistics, i.e., means and .phi..sub.0 and standard deviations
.sigma..sub.u and .sigma..sub..phi., as adjustable parameters to
model experimental results. Information about statistical
parameters can be obtained by observing the polarization dependence
of the grating. In a particular embodiment for a reflection
grating, the following values are selected for specified
parameters: n.sub.p=1.530, n.sub..perp.=1.535,
n.sub..parallel.=1.680, .alpha.=0.3, f.sub.c=0.7. For these
reflection gratings, a Bragg wavelength of 0.525 .mu.m and a
grating thickness L=8 .mu.m are selected for this specific
exemplary embodiment. For these values, the effect of an electric
field on the spectral diffraction efficiency of a Bragg grating
with light at normal incidence is illustrated in FIG. 9. For this
example, the mean droplet director is at .pi./2 radians with
respect to the grating vector (i.e., with respect to the z axis,
=0) with an isotropic distribution of droplet directors in the xy
plane (see FIG. 7c). The standard deviation .sigma..sub.u was
selected to be 0.3. This implies that the droplet directors exhibit
a preferential ordering tangential to the grating plane. This seems
be a tendency of the Merck TL series of LCs (e.g., TL213). Symmetry
about the grating vector would seem to imply that there should be
no preferential direction of ordering in the plane of the grating.
Therefore, at normal incidence the diffraction efficiency should be
independent of polarization. Switching occurs for an applied field
.about.E.sub.c. As the grating switches, the peak of the reflection
notch shifts toward the blue. This is due the field dependence of
n.sub.y (or n.sub.x), which decreases with increasing field (see
Eqs. (1), (5), (6), and (13)).
[0069] The width of p(u) has a noticeable effect on the sharpness
of the switching curve. This is illustrated in FIG. 10 where the
peak diffraction efficiency for .theta..sub..rho.=0 is plotted as a
function of field using different values of the standard deviation
.sigma..sub.u. Although the maximum diffraction efficiency at E=0
is affected somewhat, the more dramatic effect appears in the
sharpness of the switching. Therefore, observing the form of an
experimental switching curve allows one to draw an inference about
the statistics of the initial droplet-director orientation
distribution. The diffraction efficiency approaches a minimum
asymptotically for increasing field strength. The minimum is near
but not quite zero because the average droplet index approaches
n.sub..perp., which is approximately equal to n.sub.p. If
n.sub..perp.=n.sub.p, then the asymptote would be zero. This
switching by inducing a match of LC droplet index to polymer index
is the classical type of switching observed in ordinary PDLCs and
is called index switching.
[0070] Alternatively, examining the same reflection grating at
off-normal incidence, the plot in FIG. 11 shows peak diffraction
efficiency as a function of applied field for s-polarized,
p-polarized, and unpolarized light. All of the parameters are the
same as previously given, with the exception that the angle of
incidence is .theta..sub..rho.=0.1.pi.(18.degree.). FIG. 11
illustrates the difference in switching behavior between normal and
off-normal incidence. A true zero in diffraction efficiency is
achieved for p-polarization near E.sub.c, with efficiency then
showing an increase as the field is increased further. The
diffraction efficiency for s-polarized light exhibits an asymptotic
behavior similar to that seen at normal incidence. For unpolarized
light, an average of the two curves for s and p polarization is
displayed. It is difficult to obtain good switching behavior, i.e.,
high dynamic range, using unpolarized light at off-normal incidence
because of the disparity between s-polarization and p-polarization,
consequently, in a preferred embodiment, p-polarized light may be
used to yield the highest dynamic range.
[0071] The results given above are due to the tensor nature of the
grating. For s-polarization, the switching is asymptotic and based
on index switching as described above, where for large field values
the droplet index is .about.n.sub..perp..apprxeq.n.sub.p. However,
the case for p-polarization is quite different and cannot be
described as an index matching. Referring to Eq. (19), the
condition for the coupling coefficient .kappa..sub.p to vanish
is
tan .theta. .rho. = ( xx ( 1 ) zz ( 1 ) ) 1 / 2 ( 23 )
##EQU00012##
and this is achieved at some particular value of E. The form of Eq.
(23) is reminiscent of the definition of the Brewster angle for
isotropic systems and has an analogous physical interpretation. For
light incident from an isotropic medium of index n.sub.1 onto an
isotropic medium of index n.sub.2, the Brewster angle .theta..sub.B
is the angle of incidence for which the reflectance of p-polarized
light is zero. This can be calculated from electromagnetic theory
and is based on the conditions dictated by Maxwell's equations at
the boundary between the two media, with tan
.theta..sub.B=n.sub.2/n.sub.1. At the Brewster angle, the rays
transmitted to and reflected from the second medium are at a right
angle. Brewster's condition has thus been given the following
interpretation. For p-polarization, dipoles, i.e., oscillating
electrons, are induced in the second medium in the plane of
incidence and perpendicular to the transmitted ray. These dipoles
radiate and create a reflected ray back into the first medium.
However, dipoles do not radiate along a direction parallel to their
direction of oscillation. At Brewster's angle, where the reflected
and transmitted rays are at a right angle, the induced dipoles
point along the direction of the reflected ray. Since they do not
radiate any energy in this direction, the reflected ray vanishes.
Although there is some controversy regarding this interpretation,
it is true that for non-conducting, non-magnetic media, the only
work term in the electromagnetic energy theorem that could
contribute to the generation of an electric field E is the term
proportional to Re(i.omega.EP*), where P is the dielectric
polarization induced in the medium. If E and P are orthogonal, the
work term is zero and no energy can be expended to generate the
field E, even though the wave associated with E satisfies the
boundary conditions. This certainly applies to the situation of
Brewster's law in isotropic media.
[0072] Applying a similar interpretation to Bragg diffraction in
anisotropic media, in Eq. (19), the quantity .di-elect
cons..sup.(1) .sub..rho. is a vector pointing in the direction of
the spatially modulated part of the dielectric polarization induced
by the reference field E.sub..rho.. If this vector is perpendicular
to .sub..sigma., there can be no work done by the induced
polarization to generate the signal wave E.sub..sigma., even though
the direction of this wave is consistent with the Bragg condition,
and the coupling coefficient consequently vanishes. This occurs in
unslanted isotropic gratings at an incident angle of .pi./4 where
the induced polarization, in this case parallel to the reference
field, is perpendicular to the signal field. For p-polarization the
condition .sub..sigma..di-elect cons..sup.(1) .sub..rho.=0 is
equivalent to the condition given by Eq. (23), which is induced by
the applied field. Hence the applied field induces a dielectric
polarization orthogonal to the signal field to produce a zero in
the diffraction efficiency, and this is called polarization
switching.
[0073] Polarization switching of p-polarized light can be put to
use in making an inverse mode HPDLC switchable reflection grating.
An inverse mode grating is one for which the diffraction efficiency
turns on to a high value when a voltage is applied. In normal mode
HPDLC gratings a voltage turns the grating off (low diffraction
efficiency). An inverse mode grating would be advantageous for
certain applications, but is difficult to make using present
materials. The concept is to orient the diffraction grating so that
the internal incident angle of p-polarized light satisfies Eq. (23)
at zero field. Thus the diffraction efficiency would be zero. When
a field is applied, .di-elect cons..sub.zz.sup.(1) increases while
.di-elect cons..sub.xx.sup.(1) decreases. By Eq. (19), the coupling
coefficient increases and the grating turns on. An example of the
switching of s-polarized and p-polarized light for such a situation
is illustrated in FIG. 12. The conditions for this plot are:
n.sub.p=1.530, n.sub..perp.=1.530, n.sub..parallel.=1.750,
.alpha.=0.5, f.sub.c=0.9, L=15 .mu.m, .lamda..sub.B=0.525 .mu.m,
.theta..sub..rho.=0.188 .pi. (33.8.degree.), =1, .sigma..sub.u=0.4,
q(.phi..sub.0)=0.5 (isotropic .phi..sub.0-distribution). The
grating is turned on for p-polarized light and off for s-polarized
light at E.about.E.sub.c. Hence the grating is in the inverse mode
for p polarization and normal mode for s polarization.
[0074] A grating device as described herein can function as an
electro-optical polarizing beam splitter. For example, at zero
field incident unpolarized light would be split into s-polarized
light, i.e., reflected and p-polarized light, i.e., transmitted.
For an applied field >E.sub.c, the opposite effect would be
achieved: unpolarized light would be split into s-polarized light
that is now transmitted and p-polarized light that is now
reflected.
[0075] In a first embodiment of the present invention, a system and
method for controlling index modulation through nematic director
control, is described. For given LC birefringence and volume
fraction, the index modulation can be maximized by maximizing the
birefringence of the LC droplets. This is achieved by distorting
the droplets and aligning the symmetry axes of each droplet in the
same direction, which matches the polarization direction of the
incident light. It is possible to do this by applying external
stimuli that shape and orient the droplets as they are formed in
the phase separation process. Techniques for achieving this using a
magnetic field or an externally applied stress are disclosed in
U.S. Pat. No. 5,942,157 to Sutherland et al., which is incorporated
herein by reference in its entirety.
[0076] This first embodiment describes a method for distorting the
droplets and aligning the symmetry axes of each droplet in the same
direction using an electric field that is compatible with
subsequent electrical switching of the HPDLC optical device. The
pre-polymer/LC material is placed between glass plates with
transparent electrodes as disclosed in U.S. Pat. No. 5,942,157.
However, instead of transparent planar electrodes, the electrodes
are patterned as illustrated in FIG. 13a. These are called
interdigitated electrodes 30 or finger electrodes, with finger
height h 32 and finger separation b 34. These electrode parameters,
h and b, are adjusted for optimum performance. While these
parameters may vary between device applications, an exemplary
dimension is approximately 10 .mu.m for both h and b, according to
the relationship that the dimensions are approximately equivalent
in size to the thickness of the HPDLC material. Both glass plates
36a and 36b are configured with interdigitated electrodes 30a and
30b, but the back plate 36b electrodes 30b are staggered with
respect to the front plate 36a electrodes 30a as illustrated in
FIG. 13b. In an alternative embodiment, the back electrode could be
a solid planar electrode (not shown). The pre-polymer LC material
38 is irradiated holographically as disclosed in U.S. Pat. No.
5,942,157 to form either a reflection or transmission hologram (not
shown). However, while the system is being cured, a voltage (V) 39
approximately equal to the switching voltage of the device is
applied to every other finger electrode, with the same pattern
applied to both front and back electrodes 30a and 30b. This is
illustrated in FIG. 13b along with the resulting electric field
pattern. The fringing fields 40 of each electrode superpose in the
holographic medium to create an in-plane electric field 42. This
field orients the LC nematic directors 20 in the forming droplets
44 along the same in-plane direction as the resulting electric
field 42. This will also slightly distort the droplets in this
direction, making it the elastically favored direction at
equilibrium. When the system reaches gelation and the voltages 39
are removed, this orientation is locked in place. The resulting
index modulation is maximized for incident light polarized in the
same direction.
[0077] Alternatively, by applying different voltages, various
degrees of polarization state between the parallel to the film
plane to the perpendicular to the film plane may be achieved. The
applied voltages are determined by the switching voltage and are
approximately equal thereto. For light polarized in the direction
of the LC droplet symmetry axes thus formed, the index modulation
and hence the diffraction efficiency will be maximized. Light
polarized perpendicular to this direction will have minimum
diffraction efficiency.
[0078] To switch a hologram "off" that is recorded in this manner
(i.e., to zero out or minimize the index modulation), the
approximate switching voltage (V) 39 is now applied to each finger
electrode in the front set of electrodes 30a, with the back set of
electrodes 30b being connected to ground. This produces the
film-normal field pattern 46 illustrated in FIG. 14. The LC droplet
symmetry axes of the switchable HPDLC material 48 are thus
reoriented in this direction, which produces the minimum index
modulation to incident light as illustrated in the figure. This
electrode configuration can also be used to optimize temporal
response as discussed further below.
[0079] In a second embodiment of the present invention, a system is
described for controlling index modulation through fringe stability
and/or contrast control. Achieving excellent fringe stability and
contrast in the interferogram applied to the HPDLC material
optimizes index modulation in holography. Fringe contrast is
degraded by internal Fresnel reflections in the cell containing the
HPDLC material. These reflections also lead to the formation of
cross gratings as the main hologram is recorded, which contribute
to haze and cosmetic defects and decrease index modulation. The
primary source of these reflections is at the interface between the
transparent electrode (i.e., indium tin oxide (ITO)) and the
pre-polymer LC material. To alleviate this problem, a broad band
anti-reflection (AR) coating is incorporated into the transparent
electrodes. The term AR coating refers to a substantially
transparent multilayer film that is applied to optical systems
(e.g., surfaces thereof) to substantially eliminate reflection over
a relatively wide portion of the visible spectrum, and thereby
increase the transmission of light and reduce surface reflectance.
Known anti-reflection coatings include multilayer films comprising
alternating high and low refractive index materials (e.g., metal
oxides) as described, for instance, in U.S. Pat. Nos. 3,432,225,
3,565,509, 4,022,947, and 5,332,618 which are incorporated herein
by reference in their entireties. In cases of the present invention
where etching of the transparent electrode is not necessary, an AR
coating is obtained by a thin film stack of alternating layers of
magnesium fluoride and ITO applied to the glass on the side facing
the pre-polymer LC material. For cases where etching of the ITO is
desired, the preferred AR coating is a thin film stack of tantalum
oxide/magnesium fluoride deposited on the glass with an ITO
overcoat. In addition, during the recording process, an AR-coated
piece of glass is optically connected to the outside faces of the
holographic cell using index-matching fluid. These AR coatings are
optimized for the wavelength used in recording the hologram. One
skilled in the art recognizes the variations in AR coating that may
be alternatively used in this embodiment of the present
invention.
[0080] In a third embodiment of the present invention, haze and
cosmetic quality, and diffraction efficiency are controlled through
pre-establishment of a loosely gelled network in the PDLC recording
medium. As mentioned earlier, the rapid polymerization and elastic
relaxation of the multi-functional acrylate system can lead to
instability and non-uniformity in the optical quality of the
hologram, as illustrated by the example in FIG. 15 for a
transmission hologram. The two-lobed 49 "walnut-shaped" pattern
observed in FIG. 15 is a result of the instability described above.
This is related to the rapid formation of a gel network in this
free-radical system and non-uniform shrinkage of the polymer set in
place by the formation of the hologram. In reflection holograms,
this non-uniform shrinkage leads to non-uniform chirp and tapering
of the index modulation, producing a broadening of the diffraction
notch, a reduction of the peak diffraction efficiency, and a
washing out of the sidelobes. Consequently, in this third
embodiment of the present invention, a pre-establishment of a
loosely gelled network prior to hologram recording is accomplished
in a variety of ways. This loosely gelled network is (a) not so
stiff that it inhibits the diffusion of components and subsequent
phase separation which are crucial to the formation of a switchable
H-PDLC hologram, but (b) is sufficiently strong to stabilize the
system and prevent shrinkage instabilities from setting in as the
hologram begins to form. One way to accomplish this, for example,
is by blocking one of the two beams utilized in the recording setup
for a period of approximately 2-5 seconds so that the first
exposure of the sample is a beam of uniform amplitude and phase
that irradiates the sample uniformly, such that this radiation
partially bleaches the photoinitiator dye uniformly throughout the
sample. This partial bleaching can also be done by blocking both
coherent beams and irradiating the sample with an incoherent beam
of radiation. This partial bleaching of the photoinitiator
establishes a loose gel network. After this process, both coherent
beams are unblocked so that the sample is irradiated
holographically in the usual manner. The hologram is then recorded
in an identical manner as previously described in, for example,
U.S. Pat. No. 5,942,157. The result is a switchable hologram of
high diffraction efficiency and excellent optical as well as
cosmetic quality, with uniform diffraction efficiency across the
sample.
[0081] As an alternative to the photoinitiator partial bleaching
technique above, wherein the photoinitiator matched to the
recording wavelength is partially bleached, additional
photoinitiators can be added to the pre-polymer material so that
pre-establishment of the loosely gelled network can be accomplished
using illumination by a wavelength that does not overlap with the
absorption spectrum of the photoinitiator matched to the laser
recording wavelength. Examples may include using ultraviolet ("UV")
initiators to expose the PDLC recording medium for short periods of
time with UV illumination, or using visible initiators that do not
interfere with hologram recording. A specific example includes
adding methylene blue to a sample to be recorded with 488-nm light
from an argon-ion laser. This sample is exposed 632.8 nm light from
a He--Ne (helium neon) laser prior to holographic recording without
bleaching the initiator that is sensitive to the 488-nm
radiation.
[0082] It is understood that the pre-establishment of a loosely
gelled network is not limited by the radiation exposure methods
described above. Any technique to gently and partially cure the
sample so that a loose gel network is established is contemplated
by this disclosure. These techniques are known to those in the art
of polymer chemistry and may include heat, electron beams, or the
presence of other reactants that can be triggered by some external
mechanism. The third embodiment describes the formation of a
loosely gelled network prior to hologram recording in order to
stabilize the system against non-uniform shrinkage as the hologram
forms during a subsequent photopolymer chemical reaction.
[0083] Another alternative method commensurate with the scope of
the third embodiment comprises loading the pre-polymer PDLC
recording medium into a pre-existing loose network, such as an
aerogel. An aerogel is a glass or polymer network that consists
mostly of air voids that are much larger than a typical grating
period or LC droplet in an H-PDLC. The pre-polymer PDLC recording
medium fills the voids by capillary action. Such a filled aerogel
is then sandwiched between two ITO-coated glass plates and
irradiated holographically in the manner described previously. The
aerogel does not prevent diffusion of components or subsequent
phase separation of LC droplets in the grating planes, but acts
analogously to the loosely gelled polymer network of the previous
examples to stabilize the system against non-uniform shrinkage.
[0084] This technique of pre-establishment of a loosely gelled
network in the sample can be applied to transmission and reflection
gratings alike. This technique decreases the haze, improving the
optical quality of holograms. Further, this technique stabilizes
the system to shrinkage normal to the plane of the film, which
reduces chirping of the grating period and tapering of the index
modulation profile. This enhances the diffraction efficiency of the
hologram. An example of improvement of the diffraction efficiency
in a reflection hologram using this technique by partial bleaching
of the photoinitiator is given in FIG. 16.
[0085] In a fourth embodiment of the present invention, haze and
cosmetic quality are controlled using index matching and scattering
control. Significant cosmetic inhomogeneity and haze can be
attributed to the presence of cross-gratings that appear as a
result of reflections from the internal and external surfaces of
the HPDLC optical device during recording of the hologram. These
reflections interfere with both the incident beams and other
reflections, thus recording unwanted holograms in the HPDLC film.
In order to minimize these unwanted reflections, conductive
index-matched transparent electrodes as described with reference to
the third embodiment are utilized. This greatly reduces unwanted
internal reflections. These anti-reflective electrodes reduce
reflection from the internal surfaces. Second, a transparent tank
recording setup is employed to greatly reduce reflections from the
external surfaces.
[0086] Unwanted reflections at the glass/air interfaces are
rendered harmless by the transparent tank arrangement depicted in
FIG. 17. It is widely known in the holographic industry that these
reflections are troublesome, thus many organizations record
holograms in tanks of index-matching fluid. While this approach can
be effective, it is labor-intensive and requires extensive clean
up. In addition, with PDLC materials, index-matching fluid can
dissolve the LC, and therefore the cells must be completely sealed
if such an approach is to be used. The transparent tank arrangement
50 depicted in FIG. 17 uses prisms 52 or glass blocks and neutral
density (ND) filters 54 to stop unwanted reflections from exposing
the holographic cell 56. In a specific embodiment, two custom BK-7
blocks 52 possessing the same refractive index as the HPDLC optical
device 56 are manufactured to provide a particular holographic
geometry known to those skilled in the art. A HPDLC optical device
56 is placed in optical contact between the two blocks, usually
with a drop or two of index-matching fluid. If a switchable HPDLC
hologram is to be recorded, anti-reflective transparent electrodes
are used.
[0087] As with a bare cell, the reflection at either first
glass/air interface 58 is reflected safely away. In FIG. 17 the
first glass/air interfaces 58 are angled at 13.degree. and
19.degree., respectively. The reflection most problematic is the
second surface reflection which, in a bare cell, travels back
through the film. ND filters 54 are placed in optical contact at
the second glass/air interfaces, separated by index matching fluid
60, opposite the 13.degree. and 19.degree. angled faces, where the
recording beams 62 exit. Here, the ND filters 54 safely absorb the
recording laser beams 62 before a significant reflection occurs.
One skilled on the art recognizes the various optical densities
that are available for use as ND filters (e.g., 3 OD). With this
arrangement, only a few drops of index matching fluid are needed,
less if the ND filters are bonded to the block. Thus, this
arrangement represents an improvement over the use of an entire
tank of index-matching fluid, especially considering the
vulnerability of the HPDLC optical device to these fluids.
Utilizing the transparent tank arrangement 50, baseline
transmission of HPDLC holograms can be increased by a significant
percentage, e.g., as much as 10-15%. This means less haze, less
backscatter, and a cosmetically improved HPDLC optical device. The
negation of unwanted secondary gratings leads to an improved
diffraction efficiency.
[0088] According to a fifth embodiment of the present invention,
switching voltage can be controlled via tailoring of LC droplet
size and shape. By way of background, switching is best discussed
in the context of a simple model. According to U.S. Pat. No.
5,942,157, the switching voltage of a switchable hologram is
related to the critical electric field (E.sub.c) necessary to
reorient the LCs. This critical field is given by the following
equation:
E c = 1 3 a ( .sigma. LC .sigma. p + 2 ) [ k _ ( 2 - 1 ) .DELTA. ]
1 / 2 ( 24 ) ##EQU00013##
Equation (24) predicts the critical field for an elongated LC
droplet, with semi-major axis a, semi-minor axis b, and aspect
ratio l=a/b. Further to equation (1), .sigma..sub.LC and
.sigma..sub.p are the electrical conductivities of the LC and
polymer, respectively; k is an average elastic force constant while
.DELTA..di-elect cons. is the dielectric anisotropy, both
considered constant properties of the bulk LC. This equation can be
used to identify properties to target for reducing the switching
voltage. The aspect ratio l can be controlled, but may be traded
off against other parameters, e.g., polarization dependence or
index modulation. The same elongated droplet model leading to
Equation (24) predicts a relaxation time, when the applied field is
turned off, given by
.tau. off = .gamma. 1 a 2 k _ ( 2 - 1 ) ( 25 ) ##EQU00014##
where .gamma..sub.1 is the rotational viscosity coefficient of the
LC. Thus, a reduction in the effective elastic force constant that
produces a reduction in the critical field by a factor of M will
tend to increase the relaxation time by a factor of M.sup.2. If the
longer relaxation time is still compatible with the switching time
needed for a particular application, then the slower relaxation is
not a severe penalty. However, there may be cases where a longer
relaxation time is not desired.
[0089] The limiting speed of the switchable hologram is given by
the relaxation time .tau..sub.off given by Equation (25) above. Two
important geometrical parameters are droplet size a and shape l.
Droplet size a also impacts scattering loss; the scattering
coefficient increases with size approximately as a.sup.3. There is
also a trade-off of switching voltage with relaxation time as seen
in Equation (24). It is clearly desirable to keep a as small as
possible. Since scattering and relaxation time are approximately
proportional to a.sup.3 and a.sup.2, respectively, while switching
voltage is proportional to a.sup.-1, much is to be gained by
minimizing a. Ultimately, though, this will begin to increase
switching voltage unfavorably, even when optimizing matrix
conductivity, interfacial anchoring, and effective dielectric
anisotropy. At some point it is desirable to offset decreases in a
with some other parameter.
[0090] One such off-set parameter is the droplet shape. Changes in
size (.DELTA.a/a) can be approximately offset by corresponding
changes in shape (.DELTA.l/l), as can be seen by reference to
Equations (24) and (25). Distorting droplets while they are being
formed during phase separation can control droplet shape. It is
generally desirable to induce distortion (i.e., elongation) in a
direction parallel to the holographic film plane. Techniques for
achieving this using external magnetic fields and stress fields
have been discussed in U.S. Pat. No. 5,942,157. The first
embodiment of the present invention sets forth a technique for
controlling LC droplet formation using interdigitated electrodes
and in-plane electric fields. In this embodiment, a is minimized to
reduce scatter and relaxation time. Alternatively, if it is
necessary to then increase a to optimize switching voltage, then l
can be increased simultaneously to prevent the relaxation time from
increasing. This off-setting procedure allows for LC droplet
formation that optimizes HPDLC optical device operation.
[0091] According to a sixth embodiment of the present invention,
switching speed is controllable through electrode design and
voltage drive scheme. The limiting speed of the switchable hologram
is given by the relaxation time .tau..sub.off given by Equation
(25) above. The response time (i.e., when voltage is applied) is
field dependent, however. Under conditions of optimal switching
where (2+.sigma..sub.LC/.sigma..sub.p)/3.about.1, the response time
when the critical field is applied can be estimated from
.tau. on ~ .gamma. 1 4 .DELTA. E c 2 . ( 26 ) ##EQU00015##
However, for large fields E as compared to E.sub.c
(E>>E.sub.c) the response time is approximately given by
.tau. on ~ .gamma. 1 .DELTA. E 2 . ( 27 ) ##EQU00016##
Therefore, by way of example, assuming .gamma..sub.1=0.27 kg/m-s
and .DELTA..di-elect cons.=15.3.di-elect cons..sub.0, a response
time of 10 .mu.s would require a field strength of .about.15
V/.mu.m. This analysis indicates that a fast response time would be
achievable if the hologram could be driven both "on" and "off" with
a large enough field. Pursuant to the sixth embodiment of the
present invention, this can be achieved while maintaining low power
consumption.
[0092] Referring to FIG. 18a, to drive the hologram "off," a field
perpendicular to the film plane is applied. This is done by
applying a voltage (V) 39 approximately equal to the switching
voltage to each finger electrode 30a on the front plate 36a, and
connecting the electrodes 30b on the back plate 36b to ground. This
is similar to the effect that occurs when the front and back
electrodes are planar rather than patterned, and the field that
results is illustrated through field lines 40. To drive the
hologram back "on," the previous voltage scheme is removed, and
simultaneously a new voltage scheme is applied, as illustrated in
FIG. 18b. Referring to FIG. 18b, the voltage (V) 39 on every other
finger electrode 30a on both plates 36a, 36b is approximately equal
to the switching voltage, with intermediate finger electrodes 30b
on each plate 36a, 36b being connected to ground. This produces an
in-plane electric field 42 and drives the hologram "on." Switching
back and forth between these two schemes drives the hologram "on"
and "off," with a response time in each case given approximately by
Equation (27).
[0093] Switchable HPDLC holograms are normally driven at 500-2000
Hz. The period of this waveform (0.5-2 ms) is long compared to the
desired response time of the device. Therefore, the hologram can be
overdriven in the first cycle of the waveform by a field sufficient
to produce a fast response time given by Equation (27), with the
rest of the waveform settling to a lower value .about.E.sub.c to
maintain the desired state of the hologram. This type of waveform
is illustrated in FIG. 19. In this manner, the voltage is retained
at a reasonably low value during most of the operation of the
device, with little increase in the power consumption.
[0094] The embodiments described above are not intended to be
limiting. One skilled in the art recognizes the obvious variations
and trade-offs that are included within the scope of the
embodiments set forth herein.
* * * * *